Eberhard Frederich Ferdinand Hopf (April 4, 1902 in

Salzburg Salzburg (, ; literally "Salt-Castle"; bar, Soizbuag, label=Bavarian language, Austro-Bavarian) is the List of cities and towns in Austria, fourth-largest city in Austria. In 2020, it had a population of 156,872. The town is on the site of the ...

Austria-Hungary Austria-Hungary, often referred to as the Austro-Hungarian Empire,, the Dual Monarchy, or Austria, was a constitutional monarchy and great power in Central Europe between 1867 and 1918. It was formed with the Austro-Hungarian Compromise of ...

– July 24, 1983 in

Bloomington, Indiana Bloomington is a city in and the county seat of Monroe County, Indiana, Monroe County in the central region of the U.S. state of Indiana. It is the List of municipalities in Indiana, seventh-largest city in Indiana and the fourth-largest outside ...

, USA) was a

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change. History On ...

and

astronomer An astronomer is a scientist in the field of astronomy who focuses their studies on a specific question or field outside the scope of Earth. They observe astronomical objects such as stars, planets, natural satellite, moons, comets and galaxy, g ...

, one of the founding fathers of

ergodic theory Ergodic theory (Greek: ' "work", ' "way") is a branch of mathematics that studies statistical properties of deterministic dynamical systems; it is the study of ergodicity. In this context, statistical properties means properties which are expres ...

and a pioneer of

bifurcation theory Bifurcation theory is the mathematical study of changes in the qualitative or topological structure of a given family of curves, such as the integral curves of a family of vector fields, and the solutions of a family of differential equations. Mo ...

who also made significant contributions to the subjects of

partial differential equation In mathematics, a partial differential equation (PDE) is an equation which imposes relations between the various partial derivatives of a Multivariable calculus, multivariable function. The function is often thought of as an "unknown" to be sol ...

s and

integral equation In mathematics, integral equations are equations in which an unknown Function (mathematics), function appears under an integral sign. In mathematical notation, integral equations may thus be expressed as being of the form: f(x_1,x_2,x_3,...,x_n ; ...

fluid dynamics In physics and engineering, fluid dynamics is a subdiscipline of fluid mechanics that describes the flow of fluids— liquids and gases. It has several subdisciplines, including ''aerodynamics'' (the study of air and other gases in motion) an ...

, and

differential geometry Differential geometry is a mathematical discipline that studies the geometry of smooth shapes and smooth spaces, otherwise known as smooth manifolds. It uses the techniques of differential calculus, integral calculus, linear algebra and multili ...

. The

Hopf maximum principle The Hopf maximum principle is a maximum principle in the theory of second order elliptic partial differential equations and has been described as the "classic and bedrock result" of that theory. Generalizing the maximum principle for harmonic functi ...

is an early result of his (1927) that is one of the most important techniques in the theory of

elliptic partial differential equation Second-order linear partial differential equations (PDEs) are classified as either elliptic, hyperbolic, or parabolic. Any second-order linear PDE in two variables can be written in the form :Au_ + 2Bu_ + Cu_ + Du_x + Eu_y + Fu +G= 0,\, wher ...

Biography

Hopf was born in Salzburg, Austria-Hungary, but his scientific career was divided between Germany and the United States. He received his Ph.D. in mathematics in 1926 and his ''

Habilitation Habilitation is the highest university degree, or the procedure by which it is achieved, in many European countries. The candidate fulfills a university's set criteria of excellence in research, teaching and further education, usually including a ...

'' in mathematical astronomy from the

University of Berlin Humboldt-Universität zu Berlin (german: Humboldt-Universität zu Berlin, abbreviated HU Berlin) is a German public research university in the central borough of Mitte in Berlin. It was established by Frederick William III on the initiative o ...

in 1929. In 1971, Hopf was the

American Mathematical Society The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, ...

Gibbs Lecturer.Josiah Willard Gibbs Lectures #42
AMS In 1981, he received the

Leroy P. Steele Prize The Leroy P. Steele Prizes are awarded every year by the American Mathematical Society, for distinguished research work and writing in the field of mathematics. Since 1993, there has been a formal division into three categories. The prizes have b ...

from the American Mathematical Society for seminal contributions to research.

Major publications

* * * * * * * * * * * A non-comprehensive selection of his work was published in 2002: *

Notes

External links

* *
Online list of E. Hopf's works from Göttinger Digitalisierungszentrum
{{DEFAULTSORT:Hopf, Eberhard 1902 births 1983 deaths Scientists from Salzburg 20th-century German mathematicians Topologists Austrian emigrants to Germany German emigrants to the United States

Biography

See also

Major publications

Notes

External links